Hybrid quantum annealing for price optimization under cross‑elastic demand

In highly competitive markets, optimal price setting is a key strategic lever, particularly when item demand is elastic and interrelated. Small changes in the price of one item can significantly influence the demand for others through cross-elasticities, making the search for profit-maximizing price combinations a computationally challenging NP-hard problem. This paper proposes a hybrid quantum–classical approach to address large-scale price optimization under elastic demand with cross-item dependencies. The method combines quantum annealing, executed on D-Wave’s adiabatic quantum computing platform, with classical graph-based clustering to partition the problem into smaller subproblems compatible with current quantum hardware constraints. Each subproblem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model that maximizes total profit while enforcing pricing constraints and incorporating cross-elasticity effects. The system was validated on synthetic datasets simulating item catalogs of up to 2,500 items, with varying price ranges, profit margins, and elasticity densities. Results show that the hybrid solver can deliver high-quality solutions in operationally reasonable times, outperforming pure quantum execution and achieving a substantially more favorable scalability–efficiency trade-off than classical approaches such as exhaustive search and simulated annealing. The proposed framework demonstrates the feasibility of applying quantum annealing to real-world decision-support problems in the near term, even under the technological limitations of current quantum devices. This work anticipates future enhancements in quantum hardware and provides a foundation for integrating quantum optimization into dynamic pricing strategies, allowing organizations to periodically and adaptively recalculate prices as demand patterns and market conditions evolve in commerce and e-commerce environments.